The equation of the line passing through - 4 ,   3 ,   1 , parallel to the plane x + 2 y - z - 5 =…

The equation of the line passing through -4, 3, 1, parallel to the plane x+2y-z-5=0 and intersecting the line x + 1-3=y-32=z-2-1 is
  1. x+43=y-3-1=z-11
  2. x+41=y-31=z-13
  3. x+4-1=y-31=z-11
  4. x-42=y+31=z+14

Solution

A variable point on line x + 1-3=y-32=z-2-1 is -3t-1, 2t+3,-t+2

∴DR of variable point & -4, 3, 1 is

-3t+3, 2t, -t+1

Since line is parallel to x+2y-z-5=0

∴-3t+3+4t+t-1=0

⇒t=-1

∴DR of line is 6,-2, 2 or 3, -1, 1

∴ Equation of line is x+43=y-3-1=z-11

Asked in: JEE Main 2019 (09 Jan Shift 1)

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